Problem with gravity and masses

hi guys,

I was playing around with Newton Equation F=Gm1m2/r^2

I separate Fr^2 = Gm1m2 . This is bugging me. Fr^2 is a constant for a given 2 bodies(i call Z) of masses. That means that no matter what the distance r in between the two bodies, Z doesn't change. So i take my thought alittle further. Suppose the two bodies are almost infinite small with say ... 5 and 10 mass. so Z value is 50G. Since no matter how close u put them together, the value Z doesnt' change. I put them so close together that they almost like 1 body with a total mass of 15mass. Now I imagine what if they are 7 and 8 mass. The Z value is 56G. I put them throught the same process and let them come so close together that they're almost 1 body with 15mass. Now it looks like I have two identical bodies with different Z value. It seems disturbing.

olgranpappy
Homework Helper
but "Z" doesn't mean anything unless the bodies are seperated and if you seperate them in two different ways it shouldn't be surprising that you get two different "Z values".

I guess the question is... what does Z means. lol I imagine r^2 as a square and F go up and down to have a constant volume. Though I don't know what it means, but it seems unique.

olgranpappy
Homework Helper
I guess the question is... what does Z means. lol I imagine r^2 as a square and F go up and down to have a constant volume. Though I don't know what it means, but it seems unique.
it doesn't mean a thing besides G*M_1*M_2... which has only one value for a given M_1 and M_2 but may be different for different values of M_1 and M_2... even when M_1 + M_2 =M_tot is fixed, as you see in your example. but that, too, is meaningless.

it doesn't mean a thing besides G*M_1*M_2... which has only one value for a given M_1 and M_2 but may be different for different values of M_1 and M_2... even when M_1 + M_2 =M_tot is fixed, as you see in your example. but that, too, is meaningless.

Fine! I'll keep it as an souvenir. lol

Z is a function of r. You can't say that Z is independent of r...basically, when r changes, Z changes. It's just like saying that y=Gx^2 but y doesn't change while x can, it's just completely nonsensical.